Very nice explanation that is much more accessible than what I've found in dictionary or vocabulary pages.
--- Dan Bron <[EMAIL PROTECTED]> wrote: > Short answer: > > The rank of the noun determines the items, > the rank of the verb determins the cells. > > Every noun can be thought of as a "list of > something". For example, a vector (a 1 dimensional > noun) is a list of scalars, a table (2D) is a list > of vectors, a cube (3D) is a list of tables, and so > on. The items of a noun are whatever it's a list > of. The items of a vector are scalars, the items of > a table are vectors, the items of a cube are tables, > and so on. > > Any verb can be limited to a certain rank of noun. > That is, it can be impossible for a verb to see a > noun of higher than a specific rank. For example, > + can only see scalars, because list+list makes > no sense: only scalars can be added. So, no matter > how hard you try, + will only ever see a scalar at > a time. The highest rank of noun a certain verb can > see is a "cell" for that verb. > > Of course, you can feed a verb a higher ranked > argument, in which case there will be more than one > cell, but the verb will still only see one cell at a > time. That's why list+list does work: it's > operating piecewise, adding a scalar at a time. > > A verb can have infinite (unbound) rank, in which > case ANY argument will only have one cell. Think of > the monad < (box), for example. No matter what > argument you give it, it treats that argument as an > indivisible whole, and returns it in a box. > > A verb can also define its cells in terms of the > rank of the noun, so, for example, "_1 means > "operate on rank one less than the argument", which > means "treat the argument like a list of cells", > which means "operate on the items of the argument". > So, in the special case of a verb "_1 , the items > and the cells are the same. > > Does that clarify? > > -Dan > ---------------------------------------------------------------------- > For information about J forums see > http://www.jsoftware.com/forums.htm > __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
